def get_riemann_rectangles(self,
graph,
x_range=None,
dx=None,
input_sample_type="left",
stroke_width=1,
stroke_color=BLACK,
fill_opacity=1,
colors=(BLUE, GREEN),
show_signed_area=True):
if x_range is None:
x_range = self.x_range[:2]
if dx is None:
dx = self.x_range[2]
if len(x_range) < 3:
x_range = [*x_range, dx]
rects = []
xs = np.arange(*x_range)
for x0, x1 in zip(xs, xs[1:]):
if input_sample_type == "left":
sample = x0
elif input_sample_type == "right":
sample = x1
elif input_sample_type == "center":
sample = 0.5 * x0 + 0.5 * x1
else:
raise Exception("Invalid input sample type")
height = get_norm(
self.i2gp(sample, graph) - self.c2p(sample, 0)
)
rect = Rectangle(width=x1 - x0, height=height)
rect.move_to(self.c2p(x0, 0), DL)
rects.append(rect)
result = VGroup(*rects)
result.set_submobject_colors_by_gradient(*colors)
result.set_style(
stroke_width=stroke_width,
stroke_color=stroke_color,
fill_opacity=fill_opacity,
)
return result
def get_riemann_rectangles(self,
graph: ParametricCurve,
x_range: Sequence[float] = None,
dx: float | None = None,
input_sample_type: str = "left",
stroke_width: float = 1,
stroke_color: ManimColor = BLACK,
fill_opacity: float = 1,
colors: Iterable[ManimColor] = (BLUE, GREEN),
stroke_background: bool = True,
show_signed_area: bool = True) -> VGroup:
if x_range is None:
x_range = self.x_range[:2]
if dx is None:
dx = self.x_range[2]
if len(x_range) < 3:
x_range = [*x_range, dx]
rects = []
xs = np.arange(*x_range)
for x0, x1 in zip(xs, xs[1:]):
if input_sample_type == "left":
sample = x0
elif input_sample_type == "right":
sample = x1
elif input_sample_type == "center":
sample = 0.5 * x0 + 0.5 * x1
else:
raise Exception("Invalid input sample type")
height = get_norm(self.i2gp(sample, graph) - self.c2p(sample, 0))
rect = Rectangle(width=self.x_axis.n2p(x1)[0] -
self.x_axis.n2p(x0)[0],
height=height)
rect.move_to(self.c2p(x0, 0), DL)
rects.append(rect)
result = VGroup(*rects)
result.set_submobject_colors_by_gradient(*colors)
result.set_style(stroke_width=stroke_width,
stroke_color=stroke_color,
fill_opacity=fill_opacity,
stroke_background=stroke_background)
return result
